Question

We have a box with eight green marbles, five red marbles, and seven blue marbles. We choose three marbles from the box at random without looking. Write the probability in decimal form rounded to three places. What is the probability that they will all be the same color

Answer 1

Answer: 0.089

Step-by-step explanation:

Number of combinations of n things taking r at a time :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Given : A box has eight green marbles, five red marbles, and seven blue marbles.

Total marbles = 5+8+7=20

We choose three marbles from the box at random without looking.

Number of ways to choose 3 marbles with same color :-

$^8C_3+\ ^5C_3+ ^7C_3\\\\=\dfrac{8!}{3!(8-3)!}+\dfrac{5!}{3!(5-3)!}+\dfrac{7!}{3!(7-3)!}\\\\=56+10+35=101$   (1)

Total ways to select 3 marbles from 20 marbles :-

$\dfrac{20!}{3!(20-3)!}=1140$     (2)

Now, the required probability (divide (1) by (2)):-

$\dfrac{101}{1140}=0.0885964912281\approx0.089$

Hence, the required probability : 0.089